Question

Calculate the exact value of cos(a−b) given that sin a=12/13 with π/2

Answer 1

Explanation:

`sin ~a=(12)/(13) ,(\pi)/(2) <a<\pi\\a ~is~in~2nd~quadrant.\\sin~b=(3)/(5) ,0<b<(\pi)/(2) \\b~is~in~1st~quadrant.\\cos~b=√(1-sin ^2b) \\=\sqrt{1-((3)/(5) )^2} \\=\sqrt{(25-9)/(25) } \\=\sqrt{(16)/(25) } \\=(4)/(5) ,\\cos~a=-√(1-sin^2 a) \\=-\sqrt{1-((12)/(13) )^2} \\=-\sqrt{(169-144)/(169) } \\=-\sqrt{(25)/(169) } \\=-(5)/(13) \\cos(a-b)=cos~acos~b+sin~a sin~b\\=(-5)/(13)* (4)/(5) +(12)/(13)* (3)/(5) \\=?`